The Ptolemy inequality states that for a quadrilateral which is not cyclic, Ptolemy's theorem becomes the inequality:
 |
The Ptolemy inequality is still valid when 
is a triangular pyramid
(Boomstra 1956-1957).
Ptolemy Inequality
See also
Pompeiu's Theorem, Ptolemy's Theorem, Quadrilateral, Tweedie's TheoremExplore with Wolfram|Alpha
References
Boomstra, W. "Nogmaals de stelling van Pompeïu." Nieuw Tijdschr. Wisk 44, 285-288, 1956-1957.Mathologer. "Ptolemy's Theorem and the Almagest: We Just Found the Best Visual Proof in 2000 Years." Sept. 7, 2024. https://www.youtube.com/watch?v=rr1fzjvqztY.Referenced on Wolfram|Alpha
Ptolemy InequalityCite this as:
Weisstein, Eric W. "Ptolemy Inequality." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PtolemyInequality.html